Problem with knife project tool: the result is not smooth
Check camera position

Knife projection projects rays from the camera, trough the cutting geometry, till they reach the object to cut. The more your point of view is distant from the cutting geometry or your are not perpendicular to it, the less precise the operation can be.

Imagine that you have to redraw the cutting object on the plane by hand using, for example, the grease pencil. Would you be more accurate in tracing the contour by working close to the geometry or far away?

If you take the same cutting object and run the command far away and with the camera not perpendiculart to the cutting geometry (best fitting) plane:

 

While if we get close, we would get: